Full waveform tomography is an effective method to obtain high‐resolution subsurface velocity structures. It is, however, difficult for the conventional L2‐norm‐based inversion to reach the global minimum because of cycle‐skipping problem. In this study, we investigated the feasibility of using the quadratic Wasserstein metric distance (W2 norm) as the misfit function for passive adjoint tomography. We first derived equations of the Fréchet gradient and adjoint source under W2‐norm misfit function. We then conducted numerical experiments to illustrate the effectiveness of the proposed method in avoiding cycle skipping. We finally applied the adjoint tomography to eastern Tibet and obtained a 3‐D velocity model of the lithosphere. The adjoint tomography revealed two low‐velocity channels beneath the NE and SE margins of the Tibetan plateau, which were also observed by previous studies. Our results are consistent with the lower crust flow model that was proposed to explain the deformation occurring at the two margins.